If `y` is displacement and `t` is time, unit of `(d^(2)y)/(dt^(2))` will be

Options

A. `(m^(2))/(sec^(2))`
B. `(m)/(sec)`
C. `(m^(2))/(sec)`
D. `(m)/(sec^(2))`

Answer

To determine the unit of \(\frac{d^2y}{dt^2}\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let \(y\) represent displacement. The standard unit of displacement in the SI system is meters (m).
- Let \(t\) represent time. The standard unit of time in the SI system is seconds (s).

2. **Understand the First Derivative**:
- The first derivative of displacement with respect to time is given by \(\frac{dy}{dt}\). This represents velocity.
- The unit of velocity is derived from the unit of displacement divided by the unit of time:
\[ \text{Unit of velocity} = \frac{\text{Unit of displacement}}{\text{Unit of time}} = \frac{\text{meters (m)}}{\text{seconds (s)}} = \text{m/s} \]

3. **Understand the Second Derivative**:
- The second derivative of displacement with respect to time is given by \(\frac{d^2y}{dt^2}\). This represents acceleration.
- To find the unit of acceleration, we differentiate velocity with respect to time:
\[ \frac{d^2y}{dt^2} = \frac{d}{dt}\left(\frac{dy}{dt}\right) \]
- The unit of acceleration is derived from the unit of velocity divided by the unit of time:
\[ \text{Unit of acceleration} = \frac{\text{Unit of velocity}}{\text{Unit of time}} = \frac{\text{m/s}}{\text{s}} = \frac{\text{m}}{\text{s}^2} \]

4. **Conclusion**:
- Therefore, the unit of \(\frac{d^2y}{dt^2}\) is \(\text{m/s}^2\).

### Final Answer:
The unit of \(\frac{d^2y}{dt^2}\) is \(\text{m/s}^2\).

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